Door weather strips of this type are known, for instance from U.S. Pat. Nos. 4,653,802 and 5,346,273. They provide a relatively favorable sealing performance because they doubly seal both an inner gap and an outer gap between the door sash and the body panel, but create the need to seal the base portion of the weather strip. In particular, it is necessary to prevent water from being trapped between the primary and secondary door weather strips. It was proposed in Japanese Utility Model Laid-Open Publication No. 5-68750 to abut the primary and secondary door weather strips to each other to keep water from reaching the base portions from the interface between the primary and secondary door weather strips, but after repeated deformation of the weather strips, it becomes difficult to maintain an adequate contact pressure between the primary and secondary door weather strips.
The secondary door weather strip is typically provided with a seal lip which abuts the body panel upon closure of the door as a sealing member for closing the outer gap. However, the seal lip tends to develop creases on the outer surface as a result of a buckling deformation of the seal lip. Such creases tend to trap rainwater therein, and may cause unsightly water drips on the window glass. Also, loss of continuity in the profile of the door sash and the adjacent part of the door panel may lead to aerodynamic disturbances.